### Problem StatementWhen switched on, the grinding machine accelerates from rest to its operating speed of 2940 revolutions per minute (rev/min) in 5 seconds. When switched off, it coasts to rest in 36 seconds. Determine the number of revolutions turned during both the startup and shutdown periods. Also, determine the number of revolutions turned during the first half of each period. Assume uniform angular acceleration in both cases.### DiagramThe diagram illustrates a grinding machine with a rotating wheel. There is a notation indicating the angular velocity (ω) of the grinding wheel, suggesting the machine's rotational motion.### Answers:Number of revolutions during each period.- **Startup:** Δθ = [Text Box] rev- **Shutdown:** Δθ = [Text Box] revModify the above text boxes with appropriate values as calculated or enter the corresponding input in the provided fields.**Note:** To solve the problem, apply the kinematic equations for rotational motion with uniform angular acceleration. Use the following steps to derive the required values:1. **Determine angular acceleration:** - For startup: \(\alpha_{\text{startup}} = \frac{\omega_{\text{final}}}{t_{\text{startup}}}\) - For shutdown: \(\alpha_{\text{shutdown}} = \frac{-\omega_{\text{initial}}}{t_{\text{shutdown}}}\)2. **Calculate the total number of revolutions (Δθ):** - Use the equation: \(\Delta\theta = \frac{1}{2} \alpha t^2\) - For startup and shutdown, respectively.3. **Determine the number of revolutions in the first half of each period:** - Split the total angular displacement accordingly.Assumptions and angular acceleration values will be applied to determine the required revolution numbers during startup and shutdown.

Given:N=2940 rev/mint1=5 sect2=36 sec

When switched on, the grinding machine accelerates from rest to its operating speed of 2940 rev/min in 5 seconds. When switched off, it coasts to rest in 36 seconds. Determine the number of revolutions turned during both the startup and shutdown periods. Also determine the number of revolutions turned during the first half of each period. Assume uniform angular acceleration in both cases.

When switched on, the grinding machine accelerates from rest to its operating speed of 2940 rev/min in 5 seconds. When switched off, it coasts to rest in 36 seconds. Determine the number of revolutions turned during both the startup and shutdown periods. Also determine the number of revolutions turned during the first half of each period. Assume uniform angular acceleration in both cases.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Problem Statement

When switched on, the grinding machine accelerates from rest to its operating speed of 2940 revolutions per minute (rev/min) in 5 seconds. When switched off, it coasts to rest in 36 seconds. Determine the number of revolutions turned during both the startup and shutdown periods. Also, determine the number of revolutions turned during the first half of each period. Assume uniform angular acceleration in both cases.

### Diagram

The diagram illustrates a grinding machine with a rotating wheel. There is a notation indicating the angular velocity (ω) of the grinding wheel, suggesting the machine's rotational motion.

### Answers:

Number of revolutions during each period.
- **Startup:** Δθ = [Text Box] rev
- **Shutdown:** Δθ = [Text Box] rev

Modify the above text boxes with appropriate values as calculated or enter the corresponding input in the provided fields.

**Note:** To solve the problem, apply the kinematic equations for rotational motion with uniform angular acceleration. Use the following steps to derive the required values:

1. **Determine angular acceleration:**
- For startup: \(\alpha_{\text{startup}} = \frac{\omega_{\text{final}}}{t_{\text{startup}}}\)
- For shutdown: \(\alpha_{\text{shutdown}} = \frac{-\omega_{\text{initial}}}{t_{\text{shutdown}}}\)

2. **Calculate the total number of revolutions (Δθ):**
- Use the equation: \(\Delta\theta = \frac{1}{2} \alpha t^2\)
- For startup and shutdown, respectively.

3. **Determine the number of revolutions in the first half of each period:**
- Split the total angular displacement accordingly.

Assumptions and angular acceleration values will be applied to determine the required revolution numbers during startup and shutdown.

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